• What are the observational units, variable(s), and variable type(s)?
• What did the code I used to make the plot look like?

(image source: Wikipedia)

• Recall: we summarize the distribution of one continuous variable with:
  • center (mean, median)
  • spread (standard deviation, IQR)
  • shape (symmetric/skewed, unimodal/bimodal/multimodal)
  • unusual features (gaps, outliers)
• For two continuous variables, describe:
  • direction (positive association, negative association)
  • shape (linear, curved)
  • unusual features (gaps, outliers)

ggplot() +
  geom_point(mapping = aes(x = petal_length, y = petal_width),
    data = iris) +
  ggtitle("Petal Length (cm) vs. Petal Width (cm)\nfor 150 Iris Flowers")

• direction (positive association, negative association)
• shape (linear, curved)
• unusual features (gaps, outliers)

ggplot() +
  geom_point(mapping = aes(x = petal_length, y = petal_width,
      color = species),
    data = iris) +
  ggtitle("Petal Length (cm) vs. Petal Width (cm)\nfor 150 Iris Flowers")

versicolor <- filter(iris, species == "versicolor")
ggplot() +
  geom_point(mapping = aes(x = petal_length, y = petal_width),
    data = versicolor) +
  ggtitle("Petal Length (cm) vs. Petal Width (cm)\nfor 150 Iris Flowers")

versicolor <- mutate(versicolor,
  petal_length_in = petal_length * 0.3937,
  petal_width_in = petal_width * 0.3937)
ggplot() +
  geom_point(mapping = aes(x = petal_length_in, y = petal_width_in),
    data = versicolor) +
  ggtitle("Petal Length (in) vs. Petal Width (in)")

versicolor <- mutate(versicolor,
  z_score_length = (petal_length - mean(petal_length))/sd(petal_length),
  z_score_width = (petal_width - mean(petal_width))/sd(petal_width))
ggplot() +
  geom_point(mapping = aes(x = z_score_length, y = z_score_width),
    data = versicolor) +
  ggtitle("Petal Length vs. Petal Width")

• The (almost) average of products of \(z\)-scores: \(r = \frac{\sum_{i=1}^n z^x_{i} z^y_{i}}{n - 1}\)

• Using \(z\)-scores instead of original units means \(-1 \leq r \leq 1\)
• In this case, about 0.79

cor(versicolor$petal_length, versicolor$petal_width)

## [1] 0.7866681